We establish the interior gradient estimate for general 1-D anisotropic curvature flow. The estimate depends only on the height of the graph and not on the gradient at initial time. The proof relies on the monotonicity property of the number of zeros for the parabolic equation.
@article{7464, title = {Interior gradient estimate for 1-D anisotropic curvature flow - doi: 10.5269/bspm.v23i1-2.7464}, journal = {Boletim da Sociedade Paranaense de Matem\'atica}, volume = {23}, year = {2009}, doi = {10.5269/bspm.v23i1-2.7464}, language = {EN}, url = {http://dml.mathdoc.fr/item/7464} }
Nagase, Yuko; Tonegawa, Yoshihiro. Interior gradient estimate for 1-D anisotropic curvature flow - doi: 10.5269/bspm.v23i1-2.7464. Boletim da Sociedade Paranaense de Matemática, Tome 23 (2009) . doi : 10.5269/bspm.v23i1-2.7464. http://gdmltest.u-ga.fr/item/7464/